few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Analyze, compare, create, and compose shapes.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Reason with shapes and their attributes.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Understand and apply theorems about circles.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Understand congruence in terms of rigid motions.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Visualize relationships between two-dimensional and three-dimensional objects.

Define trigonometric ratios and solve problems involving right triangles.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Understand and apply the Pythagorean Theorem.

Make geometric constructions.

Translate between the geometric description and the equation for a conic section.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Find arc lengths and areas of sectors of circles.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Understand similarity in terms of similarity transformations.

Apply geometric concepts in modeling situations.

Solve real-world and mathematical problems involving area, surface area, and volume.

Experiment with transformations in the plane.

Prove geometric theorems.

Prove theorems involving similarity.

Explain volume formulas and use them to solve problems.

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

Classify two-dimensional figures into categories based on their properties.
problem_activity: Problem 1
A small box measures 5 in. across, 8 in. deep, and 6 in. tall. A book that measures 5
$$\times$$
8
$$\times$$
1 in. fits perfectly into the bottom of the box.
[IMG]
a.   What is the volume of one book? How many books will fit into the box? What is the volume of all of the books that will fit into the box?
b.   What is the volume of the box? How is this related to the volume of one book?
c.   A medium box measures 12 inches tall. A different book with dimensions 8
$$\times$$
10
$$\times$$
1 in. fits perfectly into the bottom of the medium box. What is the volume of the medium box?
Problem 2
The same rectangular prism is positioned in two different ways, as shown below. For each prism, use the rectangular face that the prism is “sitting on” as the base of the prism.
[IMG]
For each prism, find the area of the base and multiply by the height. Show that this is the same volume as when all three dimensions are multiplied together.
Problem 3
A rectangular prism has a base area of
$${4{3\over8}}$$
inches
$${^2}$$
, a width of
$$1 \frac{1}{4}$$
inches, and a height of
$${6 {1\over2}}$$
inches. Kirby writes the equation
$$V=4\frac{3}{8}\times1\frac{1}{4}\times6\frac{1}{2}$$
to represent the volume of the prism.
Do you agree with Kirby's equation? Explain and find the volume of the prism.


correct_option_index: 19